Noncommutative maximal inequalities associated with convex functions
Operator Algebras
2014-12-31 v6 Probability
Abstract
We prove several noncommutative maximal inequalities associated with convex functions, including a Doob type inequality for a convex function of maximal operators on noncommutative martingales, noncommutative Dunford-Schwartz and Stein maximal ergodic inequalities for a convex function of positive and symmetric positive contractions. The key ingredient in our proofs is a Marcinkiewicz type interpolation theorem for a convex function of maximal operators in the noncommutative setting, which we establish in this paper. These generalize the results of Junge and Xu in the case to the case of convex functions.
Keywords
Cite
@article{arxiv.1108.2795,
title = {Noncommutative maximal inequalities associated with convex functions},
author = {Turdebek N. Bekjan and Zeqian Chen and Adam Osȩkowski},
journal= {arXiv preprint arXiv:1108.2795},
year = {2014}
}
Comments
15 pages. Title changed, reviewer's suggestions incorporated